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Asymptotic properties of absolutely continuous functions and strong laws of large numbers for renewal processes


Authors: V. V. Buldygin, O. I. Klesov and J. G. Steinebach
Translated by: The authors
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 87 (2012).
Journal: Theor. Probability and Math. Statist. 87 (2013), 1-12
MSC (2010): Primary 26A12; Secondary 26A48
DOI: https://doi.org/10.1090/S0094-9000-2014-00900-X
Published electronically: March 21, 2014
MathSciNet review: 3241442
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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper, strong laws of large numbers for renewal processes constructed from compound counting processes are studied. In particular, a strong law of large numbers is proved for renewal processes constructed from compound Poisson processes with absolutely continuous rate functions.


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Additional Information

V. V. Buldygin
Affiliation: Department of Mathematical Analysis and Probability Theory, National Technical University of Ukraine (KPI), pr. Peremogy, 37, 03056 Kyiv, Ukraine

O. I. Klesov
Affiliation: Department of Mathematical Analysis and Probability Theory, National Technical University of Ukraine (KPI), pr. Peremogy, 37, 03056 Kyiv, Ukraine
Email: klesov@matan.kpi.ua

J. G. Steinebach
Affiliation: Mathematisches Institut, Universität zu Köln, Weyertal 86–90, D–50931 Köln, Germany
Email: jost@math.uni-koeln.de

DOI: https://doi.org/10.1090/S0094-9000-2014-00900-X
Received by editor(s): February 3, 2012
Published electronically: March 21, 2014
Additional Notes: This work was partially supported by DFG grants STE 306/19-2 and STE 306/23-2
The first author is deceased.
Article copyright: © Copyright 2014 American Mathematical Society

American Mathematical Society